You are given an array of positive integers nums of length n.

A pair of non negative integer arrays (arr1, arr2) of length n is defined as monotonic if:

• arr1 is non decreasing, which means arr1[0] $\leq$ arr1[1] $\leq \dots \leq$ arr1[n - 1].

• arr2 is non increasing, which means arr2[0] $\geq$ arr2[1] $\geq \dots \geq$ arr2[n - 1].

• arr1[i] + arr2[i] $=$ nums[i] for every index i such that $0 \leq i \leq n - 1$.

Return the count of monotonic pairs of arrays (arr1, arr2). Because the answer may be very large, return it modulo $10^9 + 7$.

Constraints:

• $1 \leq n ==$ nums.length $\leq 2000$

• $1 \leq$ nums[i] $\leq 50$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

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